Hyperbolicity in 2D transition metal ditellurides induced by electronic bands nesting

Naturally occurring hyperbolic plasmonic media is rare, and was only recently observed in the 1T$'$ phase of WTe$_2$. We elucidate on the physical origin of this strong infrared hyperbolic response, and attribute it to band-nested anisotropic interband transitions. Such phenomenon does not occur in general anisotropic materials, at least not in their pristine state. However, band-nested anisotropic interband transitions can in principle be induced via proper electronic band nesting. We illustrate this principle and demonstrate a topological elliptic-to-hyperbolic transition in MoTe$_2$ via strain engineering, which is otherwise non-hyperbolic.